Title:
Constructing, characterizing, and simulating Gaussian and higher-order point distributions

Abstract: The definition and the properties of a Gaussian point distribution, in
contrast to the well-known properties of a Gaussian random field are discussed.
Constraints for the number density and the two-point correlation function
arise. A simple method for the simulation of this so-called Gauss-Poisson point
process is given and illustrated with an example. The comparison of the
distribution of galaxies in the PSCz catalogue with the Gauss-Poisson process
underlines the importance of higher-order correlation functions for the
description for the galaxy distribution. The construction of the Gauss-Poisson
point process is extended to the n-point Poisson cluster process, now
incorporating correlation functions up to the nth-order. The simulation methods
and constraints on the correlation functions are discussed for the n-point case
and detailed for the three-point case. As another approach, well suited for
strongly clustered systems, the generalized halo-model is discussed. The
influence of substructure inside the halos on the two- and three-point
correlation functions is calculated in this model.

Comments:

19 pages, 4 figures, PRE in press, now including comments on hierarchical models and a comparison of random fields vs. random point sets